Adaptive controller for a refrigeration appliance

ABSTRACT

An adaptive system for controlling a refrigeration appliance is provided. More particularly, a system for controlling the cooling of the refrigerator to achieve a desired temperature performance is provided. A variable damper and variable speed evaporator fan are used to dynamically control temperature of the freezer and fresh food compartments. A model of the refrigerator system can be used to determine the settings for the damper and evaporator fan needed to achieve the temperature performance desired.

PRIORITY CLAIM

This application claims the benefit of priority of U.S. Provisional Patent Application 61/534,595, filed Sep. 14, 2011, which is incorporated herein by reference for all purposes.

FIELD OF THE INVENTION

The subject matter of the present invention relates to a control system for operating a refrigeration appliance.

BACKGROUND OF THE INVENTION

A commonly available design for a refrigeration appliance, particularly one for consumer use, includes a cabinet that contains a freezer compartment and a fresh food compartment. These compartments may be arranged e.g., side by side or may include one over the other. In one example of a conventional design, the evaporator portion of a refrigeration loop is positioned in the freezer compartment where a fan moves air in the freezer compartment across the evaporator to freeze the contents of the freezer compartment. A damper positioned between the freezer compartment and the fresh food compartment is used to feed air over to the fresh food compartment for cooling its contents. Typically, the damper is moved between a fully open or fully closed position.

To control the refrigeration loop that provides cooling for the refrigerator, one historical approach has been the use of a bimetallic thermostat. The compressor is cycled on or off based on the temperature of the thermostat. Among several drawbacks to this approach is that the measurement of temperature is limited to a single location within the appliance, which can lead to undesirable temperature gradients within the compartments.

A modern approach to control includes the use of refrigerators having microcontrollers that execute a wide variety of various algorithms for temperature control of the appliance. For many of these algorithms, the available actuators for the control system are used as either binary state devices (on/off) or sometimes as quaternary state devices (off/low/medium/high). For example, a fan for the evaporator would either be in an “on” or “off” state. A damper would be either fully shut or fully closed. As such, the scope of these control systems and their respective algorithms is limited by operating in such finite states rather than in continuous actuation.

An additional drawback to prior algorithm-based control systems is that such are based on an assumption that for each appliance unit manufactured according to a particular design, the behavior of such appliance will be nearly identical from unit to unit. However, unit-to-unit variation in the refrigerator manufacturing process can be significant due principally to the highly variable foam injection process. In addition, some often-used components of household refrigerators are known to undergo age degradation and, therefore, do not continue to behave according to the underlying assumptions of the model used in creating the algorithm for the control system. Accordingly, an algorithm developed on one unit may not cause the same behavior in another or in the same unit several years into the future. Further, the quantity and types of food that an end user may place into a refrigerator are fundamentally unpredictable and will change the effective thermal capacities of the internal compartments. Additionally, while most modern refrigerators include automatic defrosting capabilities, the efficacy of heat transfer from the unit's cooling system to the air within the food storage compartments can degrade as frost accumulates on the evaporator coils.

Therefore, a control system for a refrigerator appliance would be useful. More particularly, a control system that can adapt to variations in the heat transfer behavior of different refrigerator units would be beneficial. A control system that also adapt to changes in e.g., the thermal capacity, operating efficiency, and other variables that can affect the heat transfer characteristics of the refrigerator would also be very useful. A refrigerator control system that can employ actuators operating in continuous or dynamic states would also be particularly beneficial.

BRIEF DESCRIPTION OF THE INVENTION

Aspects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention.

In one exemplary aspect, the present invention provides a method of operating a refrigeration appliance having a fresh food compartment, a freezer compartment, an evaporator, a variable speed evaporator fan for moving air over the evaporator, and a variable damper for controlling the flow of air from the freezer compartment to the fresh food compartment. The method includes the following steps: measuring a temperature in the fresh food compartment, T_(F); measuring a temperature in the freezer compartment, T_(Z); comparing T_(F) and T_(Z) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F,) or T_(Z)≠T_(d,Z), then determining i) the position of variable damper and ii) the speed of the evaporator fan required to reach T_(d,F) and T_(d,Z) according to a predetermined rate of temperature change in either the fresh food compartment or the freezer compartment.

In another exemplary embodiment, the present invention provides refrigerator appliance having a fresh food compartment; a freezer compartment; a refrigeration cycle that includes an evaporator; a variable speed evaporator fan operable in the speed range inclusive of zero to 100 percent; a variable position damper for controlling the flow of cooled air between the fresh food compartment and the freezer compartment, said damper operable in the range inclusive of fully closed to fully open; temperature sensors for measuring the temperature of the fresh food compartment T_(F), the freezer compartment T_(F), and the evaporator T_(E); and a controller. The controller is configured for receiving temperature measurements from the temperature sensors; comparing T_(F) and T_(F) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F), or T_(Z)≠T_(d,Z), then determining i) the position of the damper and ii) the speed of the evaporator fan required to reach T_(d,F) and T_(d,Z) according to a predetermined rate of temperature change in either the fresh food compartment or the freezer compartment.

These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

FIG. 1 provides an exemplary embodiment of a refrigerator appliance as may be used with the present invention.

FIG. 2 is a schematic view of an exemplary refrigeration cycle as may be used with the present invention.

FIGS. 3 through 8 are plots of simulated and experimental data as more fully described below.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides an adaptive system for controlling a refrigerator appliance and, more particularly, to a system for controlling the cooling of the refrigerator to achieve a desired temperature performance. A variable damper and variable speed evaporator fan are used to dynamically control temperature of the freezer and fresh food compartments. A model of the refrigerator system is used to continuously determine the settings for the damper and evaporator fan needed to achieve the temperature performance desired.

Reference now will be made in detail to embodiments of the invention, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents.

As used herein, the variables below have the following meanings or references:

T refers to temperature.

Z, as a subscript, refers to the freezer compartment.

C refers to thermal capacity (mass times specific heat).

UA is the overall mass transfer coefficient.

M, as a subscript, refers to the mullion.

d refers to the percentage of evaporator fan airflow directed to the fresh food compartment (i.e., damper command).

d, as a subscript, refers to desired e.g., desired steady state temperature.

c_(P,) is the specific heat of air.

ρ is the density of air.

Kf is the evaporator airflow coefficient.

ω is the evaporator fan speed.

A or a, as a subscript, refers to ambient.

F, as a subscript, refers to the fresh food compartment.

E, as a subscript, refers to the evaporator.

θ, refers to the controller gain.

m, as a subscript, refers to the model.

τ is a time constant.

FIG. 1 provides a front view of a representative refrigerator 10 in an exemplary embodiment of the present invention. More specifically, for illustrative purposes, the present invention is described with a refrigerator 10 having a construction as shown and described further below. As used herein, a refrigerator includes appliances such as a refrigerator/freezer combination, compact, and any other style or model of a refrigerator. Accordingly, other configurations including multiple and different styled compartments could be used with refrigerator 10, it being understood that the configuration shown in FIG. 1 is by way of example only.

Refrigerator 10 includes a fresh food storage compartment 12 and a freezer storage compartment 14. Freezer compartment 14 and fresh food compartment 12 are arranged side-by-side within an outer case 16 and defined by inner liners 18 and 20 therein. A space between case 16 and liners 18 and 20, and between liners 18 and 20, is filled with foamed-in-place insulation. Outer case 16 normally is formed by folding a sheet of a suitable material, such as pre-painted steel, into an inverted U-shape to form the top and side walls of case 16. A bottom wall of case 16 normally is formed separately and attached to the case side walls and to a bottom frame that provides support for refrigerator 10 Inner liners 18 and 20 are molded from a suitable plastic material to form freezer compartment 14 and fresh food compartment 12, respectively. Alternatively, liners 18, 20 may be formed by bending and welding a sheet of a suitable metal, such as steel. The illustrative embodiment includes two separate liners 18, 20 as it is a relatively large capacity unit and separate liners add strength and are easier to maintain within manufacturing tolerances. In smaller refrigerators, a single liner is formed and a mullion 24 spans between opposite sides of the liner to divide it into a freezer compartment and a fresh food compartment.

A breaker strip 22 extends between a case front flange and outer front edges of liners 18, 20. Breaker strip 22 is formed from a suitable resilient material, such as an extruded acrylo-butadiene-styrene based material (commonly referred to as ABS). The insulation in the space between liners 18, 20 is covered by another strip of suitable resilient material, which also commonly is referred to as a mullion 24. In one embodiment, mullion 24 is formed of an extruded ABS material. Breaker strip 22 and mullion 24 form a front face, and extend completely around inner peripheral edges of case 16 and vertically between liners 18, 20. Mullion 24, insulation between compartments, and a spaced wall of liners separating compartments, sometimes are collectively referred to herein as a center mullion wall 26. In addition, refrigerator 10 includes shelves 28 and slide-out storage drawers 30, sometimes referred to as storage pans, which normally are provided in fresh food compartment 12 to support items being stored therein.

Mullion 24 or mullion wall 26 includes a damper 50 that is opened and closed to allow cooler air from the freezer compartment 14 into fresh food compartment 12. In an exemplary embodiment of the present invention, damper 50 is a variable damper 50 meaning that its position can be dynamically adjusted between open and closed as well as all settings in between. For example, damper 50 can be set at 25 percent open, 36 percent open, 64 percent, open, and substantially all over values between 0 percent open and 100 percent open. The position of variable damper 50 can be determined by a sensor and/or e.g., the voltage or current provided to an actuator that operates damper 50. Other control configurations may be used as well.

Refrigerator 10 can be operated by a controller (not shown) or other processing device according to user preference via manipulation of a control interface 32 mounted in an upper region of fresh food storage compartment 12 and coupled to the microprocessor. The controller may include a memory and one or more microprocessors, such as a general or special purpose microprocessor operable to execute programming instructions or micro-control code associated with the operation of the refrigerator. The memory may represent random access memory such as DRAM, or read only memory such as ROM or FLASH. In one embodiment, the processor executes programming instructions stored in memory. The memory may be a separate component from the processor or may be included onboard within the processor.

The controller may be positioned in a variety of locations throughout refrigerator 10. In the illustrated embodiment, the controller may be located e.g., behind panel. In such an embodiment, input/output (“I/O”) signals may be routed between the control system and various operational components of refrigerator 10 along wiring harnesses that may be routed through e.g., the back, sides, or mullion 26. Typically, through user interface panel 26, a user may select various operational features and modes and monitor the operation of refrigerator 10. In one embodiment, the user interface panel 26 may represent a general purpose I/O (“GPIO”) device or functional block. In one embodiment, the user interface 26 may include input components, such as one or more of a variety of electrical, mechanical or electro-mechanical input devices including rotary dials, push buttons, and touch pads. The user interface panel 26 may include a display component, such as a digital or analog display device designed to provide operational feedback to a user. The user interface 26 may be in communication with the controller via one or more signal lines or shared communication busses.

In one exemplary embodiment of the present invention, one or more temperature sensors are provided to detect the temperature T_(F) in the fresh food compartment 12, the temperature T_(Z) in the freezer compartment 14, the temperature

T_(E) of an evaporator 112 (FIG. 2), and the ambient temperature T_(A). This temperature information can be provided, e.g., to the controller for use in operating refrigerator 10 as will be more fully discussed below.

A shelf 34 and wire baskets 36 are also provided in freezer compartment 14. In addition, an ice maker 38 may be provided in freezer compartment 14. A freezer door 42 and a fresh food door 44 close access openings to freezer and fresh food compartments 14, 12, respectively. Each door 42, 44 is mounted to rotate about its outer vertical edge between an open position, as shown in FIG. 1, and a closed position (not shown) closing the associated storage compartment. Freezer door 42 includes a plurality of storage shelves 46, and fresh food door 44 includes a plurality of storage shelves 48.

Refrigerator 10 includes a machinery compartment that incorporates at least part of a refrigeration cycle 100 as shown in FIG. 2. The components of refrigeration cycle 100 include a refrigerant compressor unit 100, a condenser 104, an expansion device 108, and an evaporator 112—all connected in series and charged with a refrigerant. Evaporator 112 is also a type of heat exchanger that transfers heat from air passing over the evaporator 112 to a refrigerant flowing through evaporator 112, thereby causing the refrigerant to vaporize. Evaporator fan 116 is used to force air over evaporator 112 as shown by arrow E. As such, cooled air is produced and configured to refrigerate compartments 12, 14 of refrigerator 10. In one exemplary embodiment of the present invention, fan 116 is a variable speed evaporator fan—meaning the speed of fan 116 may be controlled or set anywhere between and including 0 and 100 percent. The speed may be detected by a sensor and/or dynamically controlled through amperage or voltage. Other control configurations may be used as well.

From evaporator 112, vaporized refrigerant flows to compressor unit 100, which increases the pressure of the refrigerant. This compression of the refrigerant raises its temperature, which is subsequently lowered by passing the gaseous refrigerant through condenser 104 where heat exchange with ambient air takes place so as to cool the refrigerant. Fan 120 is used to force air over the condenser for cooling the refrigerant as depicted by arrow C. Expansion device 108 (depicted in FIG. 2 as a single valve) is used to further reduce the pressure of refrigerant leaving condenser 104 before being fed as a liquid to evaporator 112. The refrigeration cycle 100 depicted in FIG. 2 is provided by way of example only. It is within the scope of the present invention for other configurations of the refrigeration system 50 to be used as well.

For purposes of describing an exemplary embodiment of the present invention, refrigerator 10 includes a single evaporator 112 located in the freezer compartment 14, fan 116 is a variable speed fan that moves air across evaporator 112 (as previously described), damper 50 is a continuously variable damper (as previously described) that allows or restricts air flow from evaporator 112 in freezer compartment 14 to fresh food compartment 12, and compressor 100 is a single speed compressor. A single speed compressor 100 is selected for this exemplary embodiment both because the outcome of the present effort will be applicable in more situations and because the low speed limitation of variable speed compressors prohibits an adaptive controller from finding an operating condition in the continuous speed range of the compressor for many environments (i.e. the compressor's minimum speed is faster than is necessary for the cooling requirements when a refrigerator is located in a room temperature environment). In this case, compressor 100 will necessarily be operated in a binary state condition.

In order to formulate a controller for a refrigerator such as appliance 10, a model was developed beginning with the following energy balance equation:

Q _((F,Z),in) −Q _((F,Z),out) =C _((F,Z)) {dot over (T)} _((F,Z))  (1)

In equation 1, Q denotes a heat flow, C denotes a thermal capacity (specific heat times mass), T denotes a temperature, and the subscripts Z and F denote freezer and fresh food compartments 14 and 12, respectively.

The heat entering each compartment comes either from the ambient atmosphere, or from the other compartment through the mullion 24. The heat transfer from either of these sources can be represented using an overall heat transfer coefficient even though the heat transfer phenomena are complex (e.g. temperature-dependent wall conductivity, mixed convection, etc.). This gives the following equations:

UA _(Z)(T _(A) −T _(Z))+UA _(M))T _(F) −T _(Z))−Q _(Z,out) =C _(Z) {dot over (T)} _(Z)  (2)

UA _(F)(T _(A) −T _(F))+UA _(M))T _(Z) −T _(F))−Q _(F,out) =C _(F) {dot over (T)} _(F)  (3)

In these equations, UA is an overall heat transfer coefficient, the subscript M denotes the mullion 24, and the subscript A denotes ambient.

The heat actively removed from each compartment 12 and 14 must necessarily flow into the evaporator 112 as the compartments are cooled. It is assumed that this heat loss is proportional to the difference in compartment temperature and evaporator temperature and to the thermal mass flow of air into the compartment. This can be represented as:

Q _((F,Z).out) =c _(P) ρ{dot over (V)} _(F,Z)(T _(F,Z) −T _(E))  (4)

In equation 4, the subscript E denotes evaporator 112, c_(P) is the specific heat of air, ρ is the density of air, and {dot over (V)} is the volumetric flow rate of air into the specified compartment.

To relate the air volumetric flow rates to the specified actuators, it is assumed that the air flow from the fan 116 is linearly proportional to the rotational speed of fan 116. Although this may not strictly be so, it is reasonable that the flow rate is a monotonic function of fan speed.

Further, it is assumed based on in situ measurements of airflow that the damper 50 divides air leaving fan 116 into a portion that flows into the freezer compartment 14 and a portion that flows into the fresh food compartment 12. Because the entirety of the airflow within the refrigerator 10 is generated by fan 116, this provides the following actuator relationships:

$\begin{matrix} {d = \frac{{\overset{.}{V}}_{F}}{{\overset{.}{V}}_{F} + {\overset{.}{V}}_{Z}}} & (5) \\ {{k_{f}\omega} = {{\overset{.}{V}}_{F} + {\overset{.}{V}}_{Z}}} & (6) \end{matrix}$

Where Ω is the rotational velocity of fan 116, d is the percentage of the total air flow of fan 116 that is directed to the fresh food compartment 12, and k_(f) is some proportionality constant relating fan speed to airflow. Substituting equations 4-6 into equations 2-3, and rearranging to provide state equations gives the following equations:

$\begin{matrix} {{\overset{.}{T}}_{Z} = {{- {\frac{T_{Z}}{C_{Z}}\left\lbrack {{UA}_{Z} + {UA}_{M} + {\left( {1 - d} \right)c_{P}\rho \; k_{f}\omega}} \right\rbrack}} + {\frac{T_{F}}{C_{Z}}{UA}_{M}} + {\frac{T_{A}}{C_{Z}}{UA}_{Z}} + {\frac{T_{E}}{C_{Z}}\left( {1 - d} \right)c_{P}\rho \; k_{f}\omega}}} & (7) \\ {{\overset{.}{T}}_{F} = {{\frac{T_{Z}}{C_{F}}{UA}_{M}} - {\frac{T_{F}}{C_{F}}\left\lbrack {{UA}_{F} + {UA}_{M} + {d\; c_{P}\rho \; k_{f}\omega}} \right\rbrack} + {\frac{T_{A}}{C_{F}}{UA}_{F}} + {\frac{T_{E}}{C_{F}}d\; c_{P}\rho \; k_{f}\omega}}} & (8) \end{matrix}$

Equations 7 and 8 above provide the rate of change of the temperature in the freezer compartment 14 and the fresh food compartment 12, respectively. All temperatures present in the above model represented by equations 7 and 8 are available from temperature sensors that can be readily located in refrigerator 10 as previously indicated. Additionally, the model represented by equations 7 and 8 is not unique to a specific platform such a refrigerator 10 and, instead, is equally applicable to bottom-freezer, side-by-side, and top-freezer configurations provided that the selected sensors and actuators are available as set forth above.

To investigate the applicability of the model in equations 7 and 8 to a physical system, a bottom-freezer refrigerator (General Electric PFSS5PJZASS) was placed devoid of food in a temperature controlled room (32.2° C.) and set to run as commercially sold for 48 hours at each of five fresh food/freezer desired temperatures using its as-shipped temperature control algorithm. During this time, the compressor on/off state, fan speed, damper position, and each of the four thermistor readings (fresh food, freezer, evaporator, ambient) were monitored. Throughout the testing period, the doors of the unit remained closed.

After the tests were concluded, temporal derivatives of the fresh food and freezer temperatures were calculated from the time histories, and a non-negative least squares regression was performed to determine the values of thermal capacities, overall heat transfer coefficients, etc. that cause the model of equations 7 and 8 to match the collected data. Specifying that the outputs of the regression are non-negative ensures that only physically possible parameters are generated (e.g. negative heat transfer coefficients are avoided).

FIG. 3 shows the results of the model matching procedure for a commanded freezer temperature of −14.4° C. and a commanded fresh food temperature of 1.11° C. As is apparent from the figure, the form of the model represented by equations 7-8 can be made to match observed data quite excellently. Although not shown, the quality of the fits for four other experimental conditions was equally good. This analysis indicates that the models present in equations 7 and 8 can accurately model the behavior of the refrigerator system and that it is an appropriate basis for an adaptive controller.

Next, a controller was developed that can take an arbitrary refrigeration unit that behaves similarly to the assumed model set forth above to a set of commanded temperatures. A well-known model reference adaptive controller, or MRAC, was selected because it works well with the assumed model and because it allows direct specification of both the time constant of the controlled system response and the desired steady state temperature. The former quantity is useful as it can be used to limit the response speed (presumably related to energy used) in responding to a disturbance (e.g. the user opening a door or adding a hot, thermally massive load to the system). As a starting point for developing the MRAC for a refrigeration appliance, the desired model is defined as first order:

{dot over (T)} _(m,(F,Z)) =−α _(F,Z) T _(m,(F,Z)) +b _(F,Z) T _(d,(F,Z))  (9)

In equation 9, the subscript m denotes the reference model, the subscript d denotes a desired state, and a and b are parameters that describe the dynamics of the reference model. Taking the difference of equation 9 and equations 7 and 8 gives the reference model tracking error and associated derivatives:

$\begin{matrix} {\mspace{79mu} {e_{F,Z} = {T_{F,Z} - T_{m,{({F,Z})}}}}} & (10) \\ {{\overset{.}{e}}_{F} = {{{- a_{F}}e_{F}} + {\frac{T_{Z}}{C_{F}}{UA}_{M}} + {\frac{T_{F}}{C_{F}}\left\lbrack {{C_{F}a_{F}} - {UA}_{F} - {UA}_{M} - {d\; c_{P}\rho \; k_{f}\omega}} \right\rbrack} + {\frac{T_{A}}{C_{F}}{UA}_{F}} + {\frac{T_{E}}{C_{F}}d\; c_{P}\rho \; k_{f}\omega} - {b_{F}T_{d,F}}}} & (11) \\ {{\overset{.}{e}}_{Z} = {{{- a_{Z}}e_{Z}} + {\frac{T_{Z}}{C_{Z}}\left\lbrack {{C_{Z}a_{Z}} - {UA}_{Z} - {UA}_{M} - {\left( {1 - d} \right)c_{P}\rho \; k_{f}\omega}} \right\rbrack} + {\frac{T_{F}}{C_{Z}}{UA}_{M}} + {\frac{T_{A}}{C_{Z}}{UA}_{Z}} + {\frac{T_{E}}{C_{Z}}\left( {1 - d} \right)c_{P}\rho \; k_{f}\omega} - {b_{Z}T_{d,Z}}}} & (12) \end{matrix}$

Two error functions are used as candidate Lyapnuov functions with the object of developing a controller that, for a_(F,Z) positive, causes error function derivatives to have the following characteristic:

ė _(F,Z)=−a_(F,Z) e _(F,Z)  (13)

Such will force the controlled refrigeration unit to track the reference model set forth in equation 9. This can be achieved using the following controllers:

(T _(E) −T _(Z))(1−d)Ω=θ₁ T _(Z)+θ₁ T _(Z)+θ₂ T _(F)+θ₃+θ₄ T _(d,Z)  (14)

(T _(E) =T _(F))dΩ=θ_(S) T _(Z)+θ₆ T _(F)+θ₇+θ₈ T _(d,F)  (15)

In equations 14 and 15, where θ_(i) are the controller gains. Rearranging these controllers in terms of the actuators gives the following equations:

$\begin{matrix} {d = \frac{\left( {T_{E} - T_{Z}} \right)\left( {{\theta_{5}T_{Z}} + {\theta_{6}T_{F}} + \theta_{7} + {\theta_{8}T_{d,F}}} \right)}{\sigma}} & (16) \\ {\omega = \frac{\sigma}{\left( {T_{E} - T_{Z}} \right)\left( {T_{E} - T_{F}} \right)}} & (17) \end{matrix}$

where

σ=(T _(E) −T _(F))(θ₁ T _(Z)+θ₂ T _(F)+θ₃+θ₄ T _(d,Z))+(T _(E) −T _(Z))(θ_(S) T _(Z)+θ₆ T _(F)+θ₇+θ₈ T _(d,F))  (8)

When the MRAC gains take on the following ideal values:

$\begin{matrix} {\theta = {\frac{1}{c_{P}\rho \; k_{f}}\begin{bmatrix} {{UA}_{Z} + {UA}_{M} - {C_{Z}a_{Z}}} \\ {- {UA}_{M}} \\ {{- {UA}_{Z}}T_{A}} \\ {C_{Z}b_{Z}} \\ {- {UA}_{M}} \\ {{UA}_{F} + {UA}_{M} - {C_{F}a_{F}}} \\ {{- {UA}_{F}}T_{A}} \\ {C_{F}b_{F}} \end{bmatrix}}} & (19) \end{matrix}$

Substitution of equations 14, 15, and 19 into equations 11 and 12 causes all terms, save the first in each, to vanish. The error function derivatives then reduce to equation 13, the error functions are Lyapnuov stable, and the controller achieves compensated plant performance of equation 9.

If the second set of candidate Lyapunov functions V_(F) and V_(Z) are selected as follows:

$\begin{matrix} {{2\; V_{F}} = {e_{F}^{2} + {\frac{C_{F}}{c_{P}\rho \; k_{f}\gamma}\left\{ {\left\lbrack {{UA}_{M} + {c_{P}\rho \; k_{f}\theta_{5}}} \right\rbrack^{2} + \left\lbrack {{C_{F}a_{F}} - {UA}_{F} - {UA}_{M} + {c_{P}\rho \; k_{f}\theta_{6}}} \right\rbrack^{2} + \left\lbrack {{{UA}_{F}T_{A}} + {c_{P}\rho \; k_{f}\theta_{7}}} \right\rbrack^{2} + \left\lbrack {{c_{p}\rho \; k_{f}\theta_{8}} - b_{F}} \right\rbrack^{2}} \right\}}}} & (20) \\ {{2\; V_{Z}} = {e_{Z}^{2} + {\frac{C_{Z}}{c_{P}\rho \; k_{f}\gamma}\left\{ {\left\lbrack {{C_{Z}a_{Z}} - {UA}_{Z} - {UA}_{M} + {c_{P}\rho \; k_{f}\theta_{1}}} \right\rbrack^{2} + \left\lbrack {{UA}_{M} + {c_{P}\rho \; k_{f}\theta_{2}}} \right\rbrack^{2} + \left\lbrack {{{UA}_{Z}T_{A}} + {c_{P}\rho \; k_{f}\theta_{3}}} \right\rbrack^{2} + \left\lbrack {{c_{P}\rho \; k_{f}\theta_{4}} - b_{Z}} \right\rbrack^{2}} \right\}}}} & (21) \end{matrix}$

Now, taking the derivatives of equations 20 and 21 (along with algebraic manipulation leads) to the following adaptation law:

{dot over (θ)}=−γ[T _(Z) e _(Z) T _(F) e _(Z) e _(Z) T _(d,Z) e _(Z) T _(Z) e _(F) T _(F) e _(F) e _(F) T _(d,F) e _(F) ]T  (22)

In equation 22, γ is the adaptation rate that causes the MRAC gains to approach the values of equation. The value of γ can be selected e.g., arbitrarily by a system designer depending upon how quickly it is desired for the refrigerator system to reach the steady state temperature settings. The full derivation of equation 22 is omitted for the sake of brevity but would be understood by one of skill in the art using the teachings disclosed herein.

The adaptive controller of equations 16-18, the adaptation law of equation 22, and a model updating technique were all implemented in LabVIEW and executed on a pair of National Instruments CompactRIO real-time targets (NI-9073). The evaporator fan, damper, and compressor control signals, as well as the temperature sensor signals were severed from their original connections to the mainboards of a side-by-side (General Electric PSHF6MGZBEBB) and a bottom freezer refrigerator (General Electric PFSS5PJXCSS). These signals were then reconnected to the CompactRIOs.

The reference model parameters (a_(F,Z) and b_(F,Z)) were set such that the reference model had first order response with a time constant of 3 hours. The sample period of temperature acquisition and of control system execution was 30 seconds. Desired temperatures of the internal compartments were again set at 2.78° C. and −17.8° C.

The single speed reciprocating compressors were energized by a relay (on/off) controller, also executed on the CompactRIOs, operating on the measured evaporator temperature with limits set equal to those measured during the observation phase discussed above. The chosen bottom freezer had a variable speed compressor that was operated at its manufacture-specified low speed according to the same relay controller.

In the first experiment, the side-by-side was placed into a room at a temperature of 22° C. and allowed to run under the influence of the MRAC. The system temperatures were as shown in FIG. 4. In FIG. 4 (and FIGS. 5-7 that follow), the darkest line of a refrigerator-measured ambient temperature, the lightest line is freezer temperature, and the medium darkness line is fresh food temperature. Dotted lines denote the commanded fresh food and freezer temperature.

The ambient temperature sensor read higher than the actual room temperature because it was located in the vicinity of the condenser and compressor in its stock configuration. Somewhat fortuitously, the air conditioning system in the room housing this refrigerator failed at the 53 hour mark of this experiment. The temperature performance was minimally affected by the air conditioning failure. FIG. 5 displays several of the MRAC gains for the same experiment. There is a clear inflection in the evolution of some gains in response to the air conditioning failure.

Next, both refrigerators were placed into a controlled temperature chamber of 32.2° C. The side-by-side temperature performance in this experiment was nearly identical to that of FIG. 4 and so is not shown for brevity. The bottom freezer's temperature histories are shown in FIG. 6. Because the bottom freezer was operating with a variable speed compressor operating at low speed, its compressor cycling time was much greater. Although the fresh food and freezer temperatures are dominated by this cycling, the MRAC induced temperature cycling behavior similar to that achieved by the manually tuned finite state machine controller described above.

In a final experiment, fifteen 1 kg containers of a glycol/water solution at 32.2° C. were placed into each refrigerator after each came to a steady state or a limit cycle. This was meant to emulate an end user's food load. The controlled temperature response to this disturbance for the side-by-side is shown in FIG. 7 and the gain adaptation is shown in FIG. 8. In both figures, the portion of the graph shown begins when the refrigerator doors were closed after the simulated load was in place. As is apparent from the figures, the controller responds correctly and adequately to the change in thermal capacity and internal temperature due to the simulated food load.

Accordingly, from the above it is understood that the following model of a refrigerator can accurately describe the thermal dynamics of the system (i.e. the parameter values can be found such that the model matches observations).

$\begin{matrix} {{\overset{.}{T}}_{Z} = {{- {\frac{T_{Z}}{C_{Z}}\left\lbrack {{UA}_{Z} + {UA}_{M} + {\left( {1 - d} \right)c_{P}\rho \; k_{f}\omega}} \right\rbrack}} + {\frac{T_{F}}{C_{Z}}{UA}_{M}} + {\frac{T_{A}}{C_{Z}}{UA}_{Z}} + {\frac{T_{E}}{C_{Z}}\left( {1 - d} \right)c_{P}\rho \; k_{1}\omega}}} & (23) \\ {{\overset{.}{T}}_{F} = {{\frac{T_{Z}}{C_{F}}{UA}_{M}} - {\frac{T_{F}}{C_{F}}\left\lbrack {{UA}_{F} + {UA}_{M} + {d\; c_{P}\rho \; k_{f}\omega}} \right\rbrack} + {\frac{T_{A}}{C_{F}}{UA}_{F}} + {\frac{T_{E}}{C_{F}}d\; c_{P}\rho \; k_{1}\omega}}} & (24) \end{matrix}$

Further, the following controller can be used to determine the speed of evaporator fan 118 and the damper angle or setting for damper 50 to cause refrigeration systems obeying the above model (equations 21 and 22) to track the given temperature specifications:

$\begin{matrix} {d = \frac{\left( {T_{E} - T_{Z}} \right)\left( {{\theta_{5}T_{Z}} + {\theta_{6}T_{F}} + \theta_{7} + {\theta_{8}T_{d,F}}} \right)}{\begin{matrix} {{\left( {T_{E} - T_{F}} \right)\left( {{\theta_{1}T_{Z}} + {\theta_{2}T_{F}} + \theta_{3} + {\theta_{4}T_{d,Z}}} \right)} +} \\ {\left( {T_{E} - T_{Z}} \right)\left( {{\theta_{5}T_{Z}} + {\theta_{6}T_{F}} + \theta_{7} + {\theta_{8}T_{d,F}}} \right)} \end{matrix}}} & (25) \\ {\omega = \frac{\begin{matrix} {{\left( {T_{E} - T_{F}} \right)\left( {{\theta_{1}T_{Z}} + {\theta_{2}T_{F}} + \theta_{3} + {\theta_{4}T_{d,Z}}} \right)} +} \\ {\left( {T_{E} - T_{Z}} \right)\left( {{\theta_{5}T_{Z}} + {\theta_{6}T_{F}} + \theta_{7} + {\theta_{8}T_{d,F}}} \right)} \end{matrix}}{\left( {T_{E} - T_{Z}} \right)\left( {T_{E} - T_{F}} \right)}} & (26) \end{matrix}$

The gains (theta) of the controller in equations 25 and 26 are found by integrating the adaptation equation:

$\begin{matrix} {\overset{.}{\theta} = {- {\gamma \begin{bmatrix} {T_{Z}e_{Z}} \\ {T_{F}e_{Z}} \\ e_{Z} \\ {T_{d,Z}e_{Z}} \\ {T_{Z}e_{F}} \\ {T_{F}e_{F}} \\ e_{F} \\ {T_{d,F}e_{F}} \end{bmatrix}}}} & (27) \end{matrix}$

For equation 27, e_(Z) and e_(f) are defined as follows:

e _(Z) =T _(Z) −T _(m,Z)

e _(F) =T _(F) −T _(m,F)  (28)

T_(m,(Z,F)) contains the desired temperature and desired dynamics of the freezer and fresh food compartments:

$\begin{matrix} {T_{m,F} = {T_{d,F} \cdot ^{- \frac{t}{\tau_{F}}}}} & (29) \\ {T_{m,Z} = {T_{d,Z} \cdot ^{- \frac{t}{\tau_{Z}}}}} & (30) \end{matrix}$

Note that the time constants of the above equations can be arbitrarily set, but it may be desirable to make their large values so that the systems respond more slowly to disturbances or changes in desired temperature and likely save energy.

An important feature of the reference model is that it incorporates the notion of “model updating” in which T_(m,(F,Z)) are periodically reset to the measured temperatures T_((F,Z)), allowing the dynamics of reference model to influence model adaptation while the desired temperatures T_(d,(F,Z)) remain constant.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they include structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

1. A method of operating a refrigeration appliance having a fresh food compartment, a freezer compartment, an evaporator, a variable speed evaporator fan for moving air over the evaporator, and a variable damper for controlling the flow of air from the freezer compartment to the fresh food compartment, the method comprising the steps: measuring a temperature in the fresh food compartment, T_(F); measuring a temperature in the freezer compartment, T_(Z); comparing T_(F) and T_(Z) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F,) or T_(Z)≠T_(d,Z), then determining i) the position of variable damper and ii) the speed of the evaporator fan required to reach T_(d,F) and T_(d,Z) according to a predetermined rate of temperature change in either the fresh food compartment or the freezer compartment.
 2. A method of operating a refrigeration appliance as in claim 1, repeating said steps of measuring T_(F), measuring T_(Z), and comparing until T_(F)≦T_(d,F), and T_(Z)≦T_(d,Z).
 3. A method of operating a refrigeration appliance having a fresh food compartment, a freezer compartment, an evaporator, a variable speed evaporator fan for moving air over the evaporator, and a variable damper for controlling the flow of air from the freezer compartment to the fresh food compartment, the method comprising the steps: measuring a temperature in the fresh food compartment, T_(F); measuring a temperature in the freezer compartment, T_(Z); comparing T_(F) and T_(Z) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F≠T) _(d,F), or T_(Z)≠T_(d,Z), then determining the rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments, respectively; and ascertaining the difference between the actual rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments from said determining step with a desired rate of change of change of T_(F) and T_(Z) in the fresh food and freezer compartments; causing the difference from said step of ascertaining to become substantially zero by adjusting i) the position of variable damper and ii) the speed of the evaporator fan.
 4. A method of operating a refrigeration appliance having a fresh food compartment, a freezer compartment, an evaporator, a variable speed evaporator fan for moving air over the evaporator, and a variable damper for controlling the flow of air from the freezer compartment to the fresh food compartment, the method comprising the steps: measuring a temperature in the fresh food compartment, T_(F); measuring a temperature in the freezer compartment, T_(Z); comparing T_(F) and T_(Z) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F), or T_(Z)≠T_(d,Z), then using a reference model to determine the desired rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments, respectively; determining the actual rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments, respectively; and, if the difference between the desired rate of change and the actual rate of change of T_(F) and T_(Z) is not less than a predetermined value, ΔT_(THR), then, using a refrigeration appliance model to calculate the position of the variable damper, the speed of the evaporator fan, or both in order to cause the difference between the desired rate of change and the actual rate of change of T_(F) and T_(Z) to be less than a predetermined value, ΔT_(THR).
 5. A refrigerator appliance, comprising: a fresh food compartment; a freezer compartment; a refrigeration cycle that includes an evaporator; a variable speed evaporator fan operable in the speed range inclusive of zero to 100 percent; a variable position damper for controlling the flow of cooled air between the fresh food compartment and the freezer compartment, said damper operable in the range inclusive of fully closed to fully open; temperature sensors for measuring the temperature of the fresh food compartment T_(F), the freezer compartment T_(F), and the evaporator T_(E); a controller configured for: receiving temperature measurements from said temperature sensors; comparing T_(F) and T_(F) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F), or T_(Z)≠T_(d,Z), then determining i) the position of the damper and ii) the speed of the evaporator fan required to reach T_(d,F) and T_(d,Z) according to a predetermined rate of temperature change in either the fresh food compartment or the freezer compartment.
 6. A method of operating a refrigeration appliance having a fresh food compartment, a freezer compartment, an evaporator, a variable speed evaporator fan for moving air over the evaporator, and a variable damper for controlling the flow of air from the freezer compartment to the fresh food compartment, the method comprising the steps: measuring a temperature in the fresh food compartment, T_(F); measuring a temperature in the freezer compartment, T_(Z); comparing T_(F) and T_(Z) with the desired setpoint temperatures, T_(d,F) and T_(d,Z), and, if T_(F)≠T_(d,F), or T_(Z)≠T_(d,Z), then determining the rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments, respectively; and ascertaining the difference between the actual rate of change of T_(F) and T_(Z) in the fresh food and freezer compartments from said determining step with a desired rate of change of change of T_(F) and T_(Z) in the fresh food and freezer compartments; adjusting i) the position of variable damper and ii) the speed of the evaporator fan to reduce the difference between the actual rate of change of T_(F) and T_(Z) and the desired rate of change of T_(F) and T_(Z); and, repeating said steps of measuring a temperature in the fresh food compartment, T_(F), measuring a temperature in the freezer compartment, T_(Z), and comparing T_(F) and T_(Z,) until the different between the actual rate of change of T_(F) and T_(Z) and the desired rate of change of T_(F) and T_(Z) is less than a predetermined value. 